Motor torque smoothing on combustion engines by approximating a periodic waveform using sinusoids

ABSTRACT

Methods, systems, and devices for operating an internal combustion engine at a firing fraction that is less than a value of 1.0, wherein one or more cylinders of the internal combustion engine are not designated to be fired, determining a smoothing event time period where a particular one of the cylinders that have not been designated to be fired is either skipped or recharged, selecting a periodic disruptive waveform to approximate that is related to a skip or recharge event that is part of the smoothing event time period, determining a first harmonic sinusoid from a group of harmonic sinusoids that reduces the error between an approximated waveform and the disruptive waveform, determining a timeframe for utilizing the first harmonic, and actuating an additional motor to initiate a supplemental quantity of torque during the smoothing event time period based on the disruption quantity of torque.

PRIORITY INFORMATION

This application is a Continuation of U.S. application Ser. No.17/138,116, filed Dec. 30, 2020, the contents of which are incorporatedherein by reference.

TECHNICAL FIELD

The present disclosure relates to combustion engine management methods,devices, and systems and, in particular, to motor torque smoothing oncombustion engines by approximating a periodic waveform using sinusoids.

BACKGROUND

Fuel efficiency of internal combustion engines can be substantiallyimproved by varying the displacement of the engine. This allows for thefull torque to be available when needed yet can significantly reducepumping losses and improve thermal efficiency by using a smallerdisplacement when full torque is not needed. Engines that use thesetechniques are generally referred to as variable displacement engines.

One engine control approach that varies the effective displacement of anengine is referred to as “skip-fire” engine control. In general,skip-fire engine control contemplates selectively skipping the firing ofcertain cylinders during selected firing opportunities. Thus, aparticular cylinder may be fired during one engine cycle, skipped duringthe next engine cycle, and then selectively skipped or fired during thenext. In some implementations, the decision to skip or fire a cylindercan be made dynamically at each firing opportunity.

Further, in some implementations, when a cylinder is skipped,air/exhaust gas can remain in the cylinder. This can be beneficial for anumber of reasons. For example, the air/gas can act as a barrier to keepoil from leaking past the piston rings and into the cylinder chamber.Such leakage can increase oil consumption and wear on the engine, amongother issues.

Over time, if the cylinder is repeatedly skipped, the air/gas can leakout past the piston rings, leaving an inadequate amount of air/gas inthe cylinder. In such a situation, the cylinder will need to berecharged with new air. During the compression cycle of a cylinder beingskipped, the compression of the residual gases creates a torque thatslows the engine. In contrast, on a subsequent expansion stroke theenergy in the compressed gases is returned, speeding the engine.

Such skip events and recharging events cause fluctuations in enginespeed. Specifically, such skip events and recharging events cause torquefluctuations that create undesirable noise, vibration, and harshness(NVH) (e.g., vibration) and can be objectionable to an occupant of thevehicle.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a representative engine cylinder andvalve system for an internal combustion engine for use with embodimentsof the present disclosure.

FIG. 2 is a graph showing RPM disruption due to recharging events in aninternal combustion engine that may be used with embodiments of thepresent disclosure.

FIG. 3 is a schematic diagram of a representative vehicle's powercomponents for an internal combustion engine for use with embodiments ofthe present disclosure.

FIG. 4 is a graph showing an example of skip, fire, and recharging eventselections for an internal combustion engine that may be used withembodiments of the present disclosure.

FIG. 5A is another graph showing RPM disruption due to recharging eventsin an internal combustion engine that may be used with embodiments ofthe present disclosure.

FIG. 5B is a graph showing a corrected RPM achieved through use of anembodiment of the present disclosure.

FIG. 6A is a graph showing torque disruption timing and magnitude due toskip, fire, and recharging events in an internal combustion engine thatmay be used with embodiments of the present disclosure.

FIGS. 6B-6D are graphs showing torque disruption timing and magnitudedue to skip and recharging events in an internal combustion engine thatmay be used with embodiments of the present disclosure.

FIGS. 6E-6G are graphs showing torque disruption frequency and magnitudedue to skip and recharging events in an internal combustion engine thatmay be used with embodiments of the present disclosure.

FIGS. 6H-6J are graphs showing torque disruption timing and magnitudewith an emphasis on low frequencies due to skip and recharging events inan internal combustion engine that may be used with embodiments of thepresent disclosure.

FIGS. 6K-6L are graphs showing the differences between AS disruptionsand LPES disruptions and the relative size of their frequency componentsin an internal combustion engine that may be used with embodiments ofthe present disclosure.

FIGS. 7A-7K illustrate an example of an approximation technique formotor torque smoothing by building a periodic waveform using sinusoidsthat may be used with embodiments of the present disclosure.

FIG. 8 is a schematic diagram of an engine controller for an internalcombustion engine for use with embodiments of the present disclosure.

FIG. 9 is a logic diagram of a controller arranged to operate aninternal combustion engine that may be used with embodiments of thepresent disclosure.

FIG. 10 is a schematic block diagram for a smoothing controller that maybe used with embodiments of the present disclosure.

DETAILED DESCRIPTION

As discussed above, methods, systems, and devices for combustion enginemanagement for internal combustion engines using skip-fire technologyare described herein. Such embodiments can determine a torque profile ofthe skip-fire controlled engine for a number of skip or recharge events,and an additional source of power can be used to smooth the torqueprofile.

For example, one embodiment includes operating an internal combustionengine at a firing fraction that is less than a value of 1.0, whereinone or more cylinders of the internal combustion engine are notdesignated to be fired, determining a smoothing event time period wherea particular one of the cylinders that have not been designated to befired is either skipped or recharged, selecting a periodic disruptivewaveform to approximate that is related to a skip or recharge event thatis part of the smoothing event time period, determining a first harmonicsinusoid from a group of harmonic sinusoids that reduces the errorbetween an approximated waveform and the disruptive waveform,determining a phase or timeframe for utilizing the first harmonic, andactuating an additional motor to initiate a supplemental quantity oftorque during the smoothing event time period based on the disruptionquantity of torque.

In various embodiments, the supplemental quantity of torque can includepositive and/or negative torque values. The engine may be either a sparkignition or compression ignition engine. The internal combustion enginemay, for example, be used to power a vehicle.

The described approaches are particularly suitable for use in hybridvehicles in which the combustion engine is operated using a skip-fire orother variable displacement technique. In some embodiments, the vehicleincludes a motor/generator that applies the smoothing torque but is notused as a hybrid engine.

Skip-Fire Technology

Through use of skip-fire technology, fine control of the effectiveengine displacement is possible. For example, firing every thirdcylinder in a 4-cylinder engine would provide an effective displacementof ⅓ of the full engine displacement, which is a fractional displacementthat would not be obtainable by simply deactivating a set of cylinders.

U.S. Pat. No. 8,131,445 (which is incorporated herein by reference)teaches a skip-fire operational approach, which allows any fraction ofthe cylinders to be fired on average using individual cylinderdeactivation. Performing cylinder deactivation requires the enginecontroller to control power driver outputs that actuate the cylinderdeactivation elements. In other skip-fire approaches a particular firingsequence or firing density may be selected from a set of availablefiring sequences or fractions.

In a skip-fire operational mode the amount of torque delivered generallydepends on the firing density, or fraction, of combustion events thatare not skipped. Dynamic skip-fire (DSF) control refers to skip-fireoperation in which the fire/skip decisions are made in a dynamic manner,for example, at every firing opportunity, every engine cycle, or at someother interval.

Further, in some applications referred to as multi-level skip-fire,individual working cycles that are fired may be purposely operated atdifferent cylinder output levels, that is, using purposefully differentair charge and corresponding fueling levels. By way of example, U.S.Pat. No. 9,399,964 (which is incorporated herein by reference) describessome such approaches.

The individual cylinder control concepts used in dynamic skip-fire canalso be applied to dynamic multi-charge level engine operation in whichall cylinders are fired, but individual working cycles are purposelyoperated at different cylinder output levels. Dynamic skip-fire anddynamic multi-charge level engine operation may collectively beconsidered different types of dynamic firing level modulation engineoperation in which the output of each working cycle (e.g., skip/fire,high/low, skip/high/low, etc.) is dynamically determined duringoperation of the engine, typically on an individual cylinder workingcycle by working cycle (firing opportunity by firing opportunity) basis.

It should be appreciated that dynamic firing level engine operation isdifferent than conventional variable displacement in which when theengine enters a reduced displacement operational state, a defined set ofcylinders are operated in generally the same manner until the enginetransitions to a different operational state. However, the techniquesdisclosed herein can be utilized in any variable displacement enginewhere a skipped cylinder can cause a torque disturbance affecting enginespeed.

In a skip-fire engine, steady-state variations in RPM contain knownfrequency components, which can be reduced by using this knowledge tocreate a counter-torque provided by an electric motor. One way to dothis is to produce a counter-torque signal including one or moreharmonic frequencies of the length of the firing pattern. Alternatively,a predicted torque waveform can be constructed and a filtered version ofthis waveform can be used to reduce the engine speed variations.

These technologies have proven successful in some implementations ofengines that use low pressure exhaust springs (LPES) for deactivatedcylinders. However, in engines that use air springs (AS) or highpressure exhaust springs (HPES), the compression of the charge in thecylinder will require enough work, and its subsequent expansion producesenough work, that the effect can be sensed on the crankshaft because itwill cause engine speed variation.

Additionally, cylinders that use air springs require them to berecharged (vent the current charge to the exhaust manifold, and intake anew charge from the intake manifold) periodically. These recharge eventswill also be a periodic source of engine speed variation.

Current techniques do not account for engine speed variation due to:compressing or expanding cylinders containing a charge (AS or HPESmodes) or recharging a cylinder. Rather, current techniques only accountfor vibrations due to firing a cylinder and are only utilized for LPES.

One embodiment of the present disclosure involves using knowledge of theperiodicity of the firing pattern and recharging pattern to produce acounter-torque signal to reduce engine speed variation. For example, asix-cylinder four-stroke engine that idles using a firing fraction of ⅓at 600 RPM will fire a cylinder ten times per second (5 cycles persecond, firing two cylinders per cycle). Regardless of the type ofspring used (LPES, AS, HPES), this means the fundamental frequency is 10Hz, and so a 10 Hz sinusoidal excitation by the supplemental powersource can be used to reduce the engine speed variation. Higher harmonicfrequencies can also be used. The effect of the spring type (LPES, AS,HPES) is that it changes the phase and/or magnitude of the sinusoid ateach frequency can also be quantified, for example, through testing ofthe engine or sensor data during engine use and can be used in selectingthe characteristics (e.g., phase, magnitude, frequency) of the one ormore sinusoids selected.

Another sinusoid can then be added to reduce the vibration due to therecharging step. In the example above, the deactivated cylinders need tobe recharged if an air spring (or HPES) is used. If the requiredrecharge time is 20 cycles, and the recharges are distributed evenlyover time, the recharge process will cause a ¼ Hz disturbance in theengine speed, since it will take 20 cycles to recharge the fourdeactivated cylinders.

It may be beneficial to cancel harmonics of the recharging rate, eitheradditionally or instead of the fundamental depending on the NVH impactof the fundamental and/or the harmonics of the recharging rate. If therecharge events are approximately evenly spaced, for example one every 5cycles, the 4th harmonic at 1 Hz for this example may be particularlystrong and may be worth reducing or removing even without other harmonicconsiderations.

Some embodiments disclosed herein include constructing predicted torqueprofiles given the firing-skip pattern/history, spring type, and/orrecharge pattern. For example, the torque output from a firing cylindercan be well modeled given the criteria of the amount of fuel burned andthe engine speed. In some embodiments, the torque loss due to arecharging event can be similarly modeled based on engine speed, intakemanifold pressure (IMP), and exhaust manifold pressure (EMP), as well asthe spring-effect and spring mode used, including the decay of thespring after it is recharged. In some embodiments, the resulting torquewaveform can be filtered to remove desirable components, like theaverage torque or DC term, and less important components, like highfrequency terms that produce less NVH. The resulting filtered torquesignal can then be inverted and the controller of the supplemental powersource uses it as a command input to produce the smoothingcounter-torque.

Such embodiments can, for example, reduce the amount of engine speedvariation, which is perceived by an occupant of a vehicle as NVH. Adiscussion of the formation of canceling waveforms from multiplesinusoids is provided with respect to FIGS. 7A-7K below.

In the following detailed description, reference is made to theaccompanying drawings that form a part hereof. The drawings show, by wayof illustration, how one or more embodiments of the present disclosuremay be practiced.

These embodiments are described in sufficient detail to enable those ofordinary skill in the art to practice one or more embodiments of thepresent disclosure. It is to be understood that other embodiments may beutilized and that process, computerized, and/or structural changes maybe made without departing from the scope of the present disclosure.

As will be appreciated, elements shown in the various embodiments hereincan be added, exchanged, combined, and/or eliminated so as to provide anumber of additional embodiments of the present disclosure. Theproportion and the relative scale of the elements provided in thefigures are intended to illustrate the embodiments of the presentdisclosure and should not be taken in a limiting sense.

The figures herein follow a numbering convention in which the firstdigit or digits correspond to the drawing figure number and theremaining digits identify an element or component in the drawing.Similar elements or components between different figures may beidentified by the use of similar digits. For example, item “20” may bereferenced as element “120” in FIG. 1, and a similar element may bereferenced as “220” in FIG. 2.

As used herein, “a” or “a number of” something can refer to one or moresuch things. For example, “a number of valves” can refer to one or morevalves. As used herein, “a plurality of” means two or more things.

FIG. 1 is a schematic diagram of a representative engine cylinder andvalve system for an internal combustion engine for use with embodimentsof the present disclosure. As shown in FIG. 1, an internal combustionengine has a number of cylinders 100 that mix fuel and air together andcombust the mixture to provide power to a driveshaft (e.g., which turnsthe wheels that move the wheels of an automobile).

The mixing occurs within a cylinder chamber 114 of the cylinder 112. Airenters the cylinder chamber 114 through intake 102 that includes anintake valve 104 to open and close access between the intake and thecylinder chamber.

A piston 110 within the chamber compresses the fuel/air mixture (or justair in Diesel engines, as the fuel is added to the compressed air) andthen the fuel/air mixture is ignited. This combustion event pushes thepiston from its compression position 120 to its uncompressed position122 and also pushes the arm 124 connecting to the crankshaft (which isnot shown and is connected to the driveshaft, also not shown). Thecombusted air/fuel mixture (exhaust) is then pushed out of the cylinderchamber and into the exhaust system 106 as the piston 110 is moved backup to the compression position 120 with the exhaust valve 108.

Spring-Like Forces within the Cylinder

In a variable displacement engine system when a cylinder is skipped andthere is air/gas in the cylinder, the remaining air/gas is trappedwithin the cylinder chamber and provides a spring-like force whencompressed by the piston. For example, when the intake valves and theexhaust valves are not open, the compression by the piston creates aspring-like effect that acts to push the piston toward its uncompressedcondition.

Using this mechanism, three kinds of spring-like effects can be created.A first is called a low pressure exhaust spring (LPES) force. In thistype, after the firing of the cylinder (igniting of the fuel/air mixturein the cylinder chamber) is finished, the remaining gases are exhaustedfrom the cylinder chamber so that the cylinder chamber is nearlycompletely empty. The exhaust valve is then closed, and the intake valveis not opened. This configuration provides little to no torque.

The second type is called an air spring (AS) force. In this type, theexhaust (after ignition of the fuel/air mixture in the cylinder chamber)is pushed out through the open exhaust valve by the piston. However,instead of closing all valves, the intake valve is opened and air istaken into the cylinder as the piston returns to its pre-compressionposition. Then, the intake valve is closed. The air is then compressedas the piston moves toward its compressed position, and the remainingair/gas counteracts the force of the piston increasingly the more thatthe air/gas is compressed.

The third type of spring effect is called a high pressure exhaust spring(HPES) force. This happens when the combustion of the fuel/air mixtureoccurs, but some or all of the combusted gas and fuel is kept in thecylinder during a subsequent compression by the piston. This can occur,for example, where cylinder deactivation occurs after a combustion eventbut prior to an exhaust event. In such an instance, all of the exhaustremains in the cylinder during the duration of deactivation of thecylinder.

All spring types are used in different applications, with diesel enginesusing air springs (typically) while gasoline engines may often use LPESor HPES. And, although the skip process can use any of the spring modesdiscussed herein, typically skip processes utilize an air spring modethat includes exhausting the cylinder, pulling air into the cylinder viathe intake valve, and sealing the cylinder by closing all of the valves.This trapped air is then compressed and uncompressed as the enginecycles.

A couple of issues can arise, however, during such an air springprocess. First, the air cools. This is due to several factors. Forexample, the air heats as it is compressed, but some of that heat istransferred to the cylinder wall. The subsequent expansion does notrecover that heat.

Second, when compressed, some air will be pushed past the cylinder rings118 (that form a seal between the ring surface and the cylinder chamberwall 116) that are supposed to trap the air in the cylinder. This mayaccount for only a small loss during one cycle, but if it continues tooccur for several cycles, it can result in the cylinder becoming emptiedof air substantially or at least below a threshold level.

One benefit of maintaining air in the cylinder is that it keeps oil frommigrating from the crankshaft and into the cylinder. This isparticularly beneficial in Diesel engines, which typically have looserrings than gasoline engines do and are therefore more prone to oilleakage into the cylinders.

A recharge process can be implemented where the spring force has beenutilized but has weakened (e.g., due to the above leakage) and needs arecharge. Further, a recharge process can also be implemented prior toswitching a cylinder from skip mode to firing mode, for example, if ithas not been recharged for a threshold number of cycles prior to aplanned firing event. A recharge process can, for example, include:opening the exhaust valve, pushing out the exhaust gas, opening theintake valve, and pulling in air.

In one example, half of the cylinders of the engine are fired. Forexample, six cylinders with 1, 3, and 5 firing and 2, 4, and 6 skipped.The next cycle, again, cylinders 1, 3, and 5 are firing and 2, 4, and 6are skipped. In this manner, cylinders 1, 3, and 5 are always firing and2, 4, and 6 are always skipped. This can present problems, as discussedabove.

Accordingly, in some implementations, the cylinders may need to berecharged. As illustrated in the graph 445 shown in FIG. 4 and discussedin more detail below, these recharge events (denoted by a −1) can bestaggered to reduce the impact on NVH. However, even staggered overtime, the individual recharge events do impact NVH as indicated in FIG.2.

In another example, by running a firing fraction (FF) of ⅓ on a6-cylinder engine (e.g., firing cylinders 1 and 6 and deactivating theother four cylinders), the four deactivated cylinders can be recharged(rebreathed) at a predictable interval. If the recharging interval iscalibrated to a total of 20 cycles, the recharge events on the fourdeactivated cylinders can be equally spaced at 5 cycles apart (e.g., onecylinder can be recharged at each of cycles 5, 10, 15, and 20). FIG. 2,below, illustrates the RPM disruption that occurs when the cylinders arerecharged.

FIG. 2 is a graph showing RPM disruption due to recharging events in aninternal combustion engine that may be used with embodiments of thepresent disclosure. FIG. 2 shows an example of RPM fluctuations causedby recharging events on deactivated cylinders while operating a firingfraction of ⅔ on an inline, 6 cylinder engine.

In this example, there is a fixed pattern where cylinder 1 and 6 aredeactivated and the other four cylinders are active and firing in everycycle. Cylinders 1 and 6 are periodically recharged at a calibratableinterval as shown. As can be seen in this illustration, the rechargeevents 228 have a noticeable effect on the overall RPM distribution 227over time. This change in RPM distribution may be felt by the occupantsof the vehicle.

These recharge events are identified as those in which a loss of torqueis produced by the engine over a period of time (e.g., during and/orafter the recharge event). In such embodiments, a counteracting torquecan then be applied to the powertrain in a controlled manner by anenergy source at a determined timeframe during and/or after theidentified events such that the expected net powertrain torque issmoothed during the event.

In some skip-fire or other dynamic firing level modulation embodiments,the torque profile estimations are used in the selection of the(effective) operational firing fraction. In such embodiments, the fuelefficiency of various candidate firing fractions may be compared afterconsidering the fuel efficiency implications of any smoothing torquesthat may be required to meet desired drivability criteria when operatingat the respective firing fractions.

In some embodiments, the engine torque profile is filtered to identifyselected harmonic components of the torque profile. A counteractingsmoothing torque to apply to the powertrain may then be determined basedon the filtered results.

In some such embodiments, the filtered results may be amplified based onone or more current engine parameters. When it is to be applied, thetiming of the filtered signal may be delayed to align with the torquepredicted to be produced by the engine. The amplified filtered signalmay be inverted and used in the control of, for example, an electricmotor/generator to source torque based on the inverted torque signal.

In some embodiments, the smoothing torque may be applied as one or moreoscillating (e.g., sinusoidal) signals, whereas in others, the smoothingtorque may be applied as impulses intended to offset portions ofexpected torque troughs.

In various embodiments, the torque applied by devices that add torque tothe powertrain can be increased or decreased to effectively provide thedesired smoothing torque. When devices that can both add and subtracttorque are used, such as a motor/generator, either of these approachesmay be used, or the devices may be varied between torque contributingand torque drawing states to provide the desired smoothing torque.

As discussed herein, the embodiments of the present disclosure describevarious control methods in which an additional power source, in additionto the internal combustion engine, is operated in a manner thatgenerates a smoothing torque, which is applied to a vehicle powertrain.The smoothing torque is any torque that is applied to help cancel out orreduce a variation in torque associated with skipping and/or rechargingevents in an internal combustion engine.

The smoothing torque can be generated by any suitable energystorage/capture/release device. One example would be an electricmotor/generator with a battery and/or capacitor to store and releaseenergy. Alternatively, any system or device that stores andcaptures/releases energy mechanically, pneumatically, or hydraulicallymay be used.

For example, a flywheel with a variable mechanical coupling, or ahigh-pressure fluid reservoir with valves controlling fluid flow to andfrom a turbine or similar device may be used to capture/release energyfrom a powertrain. The smoothing torque is applied in a manner whichcancels out or at least partially reduces noise and vibration generatedby the recharging process.

FIG. 3 is a schematic diagram of a representative vehicle's powercomponents for an internal combustion engine. More specifically, FIG. 3illustrates an example parallel hybrid electric vehicle powertrain 330and associated components that can be used in conjunction with theembodiments of the present disclosure. However, it should be appreciatedthat the same concepts can be applied to other hybrid powertrains,including but not limited to series hybrid electric configurations,power-split electric configurations, mild hybrid with a belt drivenstarter-generator (BSG), and hydraulic hybrid configurations.

FIG. 3 shows a skip-fire controlled internal combustion engine 332applying torque to a powertrain drive shaft (not shown) which isconnected to a transmission 334, which in turn drives selected wheels340 of a vehicle. A motor/generator 338 is also coupled to thepowertrain and is capable of either simultaneously generating electricalpower (thereby effectively subtracting torque from the drive shaft) orsupplementing the engine torque, depending on whether the engine isproducing surplus torque or deficit torque relative to a desiredpowertrain torque output.

When the engine produces surplus torque, the surplus torque causes themotor/generator 338 to generate electricity which can be stored in theenergy storage device 342 after conditioning by the power electronics344. The energy storage device 342 may be, for example, a battery and/ora capacitor. The power electronics 344 may include circuitry to convertthe output voltage on the energy storage device 342 to a voltagesuitable for delivering/receiving power from the motor/generator 338.

When the engine produces deficit torque, the engine torque issupplemented with torque produced by the motor/generator 338 usingenergy previously stored in the energy storage device 342. Use of acapacitor as energy storage device 342 may lead to a larger improvementof the overall fuel economy of the vehicle by largely avoiding theenergy losses associated with charging and discharging conventionalbatteries. This is particularly advantageous when relatively frequentstorage and retrieval cycles are contemplated, as in the embodiments ofthe present disclosure.

FIG. 4 is a graph showing an example of skip, fire, and recharging eventselections for an internal combustion engine that may be used withembodiments of the present disclosure. FIG. 4 illustrates a six cylinderengine with each column representing one cylinder (1-6) over a period of60 cycles.

In the embodiment illustrated in FIG. 4, cylinders 1, 3, and 5 arealways fired, with the firing illustrated by a “1”. Cylinders 2, 4, and6 are always skipped unless they are being recharged. Skip mode isillustrated with a “0” and a recharge event is illustrated by a “−1”. Ascan be understood from this illustration, each of cylinders 2, 4, and 6are recharged three times over the 60 cycles (every 20 cycles).

As illustrated in this graph, the recharge events can be staggered foreach cylinder and with respect to the recharge events of the othercylinders. Such staggering reduces the impact on the vehicle occupant,as the events are not occurring multiple times over a short period.

FIG. 5A is another graph showing RPM disruption due to recharging eventsin an internal combustion engine that may be used with embodiments ofthe present disclosure. In a system that uses an air spring fordeactivation, a recharging event typically starts by opening the exhaustvalve first to exhaust any trapped air and then opens the intake to takein a fresh charge of air (rebreathing). The following compression strokewill have a higher negative torque due to a higher quantity of airtrapped in the cylinder compared to during the leaked-down state justprior to the rebreathing event.

With respect to recharging events, the proposed system uses feedforwardinformation from the firing fraction and recharging controller andschedules a cancelling torque generated by an additional power source inorder to cancel the torque fluctuation. Among other benefits, thisimproves smoothness of torque delivery, idle control (in idleconditions), and NVH and reduces signal fluctuations going into DSF andother closed loop control systems. In some embodiments, appropriate timedelays can be put into the additional power source control system toalign with the timing of the torque bump/torque sag to be cancelled bythe power provided by the additional power source. This time delay couldbe crank-angle-based or time-based and could also be a function ofengine speed.

It should be noted that the embodiments of the present disclosure canalso be utilized during a re-exhausting event before a fire event aftera long period of skip events (this is distinct from periodicallyrecharging a deactivated cylinder with no immediate intent to refireit). In such implementations, the exhaust and intake strokes just beforea refire also have a negative pumping torque signature that can becancelled in a feedforward manner. Further, in an alternativeembodiment, the cancellation signature can be described in terms ofharmonics in the frequency domain instead of individual time-domainpulses (time domain is shown in FIG. 5A).

To provide a cancellation instruction to the additional power source,given a firing fraction and a given number of skip cycles on a cylinderbefore recharge, the frequency of occurrence of a recharging event canbe predicted. For example, when using a FF of ⅓ on a 6-cylinder engine(e.g., firing cylinders 1 and 6 and deactivating the other fourcylinders), the four deactivated cylinders will rebreathe at apredictable interval. If, for instance, the recharging interval iscalibrated to 20 cycles, the recharge events on the four deactivatedcylinders can be equally spaced at 5 cycles apart. At an engine speed of600 RPM, this translates to a recharging frequency of 1 Hz. As such, theadditional power source torque smoothing controller can then be set tocancel this 1 Hz fluctuation using, for example, least mean squares(LMS) or recursive least squares (RLS) minimization of RPM fluctuationfeedback, among other cancellation techniques.

Transitions between FFs or between variants of the same FF can also havepredictable recharging events/frequencies. For example, toggling backand forth between ½A and ½B (½A=cylinders 1, 3, and 5 and ½B=2, 4, and6) requires three cylinders to recharge quickly one after the other inthe same cycle. Depending on the frequency of toggling, the rechargefrequency can be calculated and fed forward to the additional powersource controller (e.g., engine controller) to generate the cancellationtorque at the time of these recharge events.

In the illustration of FIG. 5A, the firing fraction is ⅔ and the enginespeed is 700 RPM. The skipped cylinders are being recharged every 20cycles but are staggered from each other. In this example, too, a dip547 in RPM 546 is visible in the data at times associated with therecharge events. Such disruptions to RPM create undesirable NVH.

To reduce or eliminate this undesirable condition, a waveform of thistorque disturbance for each recharge event can be determined if severalcriteria are known. For example, criteria that can be useful include:what the cylinders are doing during the recharge (this is dependent onthe type of spring-effect used: LPES, AS, HPES) and the torque effect ofa recharge event. Such information can be estimated or established basedupon operational data of this engine or a similar engine.

FIG. 5B is a graph showing a corrected RPM achieved through use of anembodiment of the present disclosure. In FIG. 5B, the data used todetermine the torque disturbance has been used to determine a responsefrom a secondary power source that supplements the torque provided bythe primary power source to reduce or eliminate the RPM disruptionsduring periods associated with the recharge events 549 in the RPM 548 ofthe engine. In this manner, through use of the embodiments of thepresent disclosure, the NVH impacts of the recharging events can bereduced or eliminated.

FIG. 6A is a graph showing torque disruption timing and magnitude due toskip, fire, and recharging events in an internal combustion engine thatmay be used with embodiments of the present disclosure. This graph 670illustrates types of wave disruptions each mode of operation creates andcrank angles (i.e., crankshaft angle with respect to top dead center(TDC)) (e.g., shown at 126 of FIG. 1) at which each type of disruptionoccurs.

For example, a disturbance related to a combustion event (fire) 674occurs as the cylinder approaches TDC (0 degrees) as do smallerdisturbances associated with skip 672 and recharge 676 events. A smallerdisturbance also occurs with skip events as the crankshaft angleapproaches −360. The identification of the crank angle and magnitude canbe used to determine the magnitude and timing of the actuation of thesecondary power source.

FIGS. 6B-6D are graphs showing torque disruption timing and magnitudedue to skip and recharging events in an internal combustion engine thatmay be used with embodiments of the present disclosure. FIG. 6Billustrates a graph showing the torque disruption 671 of a low pressureexhaust spring (LPES). In this implementation, the cylinder has littleto no air/gas in the cylinder chamber. In this graph, the torque outputis a uniform, repeating pattern for each cycle.

FIG. 6C illustrates a graph showing the torque disruption 673 of an airspring (AS), as discussed above. In this implementation, the cylinderhas gas in the cylinder chamber which has replaced most or all of theexhaust gas that has been pushed out of the cylinder chamber, and norecharge event is done. In this graph, the torque output is morecomplex, but is also a uniform, repeating pattern for each cycle.

FIG. 6D also illustrates a graph showing the torque disruption 675 of anair spring (AS), but in this graph, a recharge event is illustratedduring cycle 7 between 7 and 7.5. As illustrated, in this graph, thetorque output is not a uniform, repeating pattern for each cycle and thedifference shown, although subtle, may be perceptible to an occupant ofa vehicle. This is particularly the case if the disruption is a lowfrequency (e.g., below 10 Hz), which recharge events may createdepending on other engine criteria discussed below.

FIGS. 6E-6G are graphs showing torque disruption plotted showingfrequency and magnitude due to skip and recharging events in an internalcombustion engine that may be used with embodiments of the presentdisclosure. In these figures, the frequency axis is the engine order(0-6) with spikes at approximately 1.5, 3.0, and 4.5 (illustrated byelements 677, 678, and 679, respectively). Because this is asix-cylinder engine, the 3rd order 678 is present. The y-axis isnormalized to show the 1.5 order (due to the skip-fire pattern) 677 witha size of 1 in FIG. 6E. However, when an air-spring is used (in FIGS. 6Fand 6G, the relative size of the 3rd order 678 approximately doubles (tonear 2.0), creating more vibration than with the LPES and motivatingcancellation using a secondary power source. It is difficult to see thefrequency effect of recharging at this scale, because it is aninfrequent, relatively low-energy event. But, because it is lowfrequency, it is felt more easily (and is more annoying to occupants)than the higher frequency excitations from combustion and air springs.As such, it should be reduced or eliminated using this data.

FIGS. 6H-6J are graphs showing torque disruption timing and magnitudewith an emphasis on low frequencies due to recharging events in aninternal combustion engine that may be used with embodiments of thepresent disclosure.

In some implementations, the recharging event happens about once everyseven engine cycles, which is low frequency. However, as shown at 682 inFIG. 6J, as compared to lines 680 and 681 of FIGS. 6H and 61, it alsohas many higher harmonics due to the limited duration of its effect.These harmonics can also be potentially problematic from an NVHperspective. Therefore, removing disruptions from recharging may also bebeneficial for this reason.

FIGS. 6K-6L are graphs showing the differences between AS disruptionsand LPES disruptions and the relative size of their frequency componentsin an internal combustion engine that may be used with embodiments ofthe present disclosure. FIG. 6K illustrates the difference betweenengine disruptions of an engine using an air spring (top graph) and onethat does not (LPES in bottom graph).

As can be seen from these graphs, the AS disruption is a much morecomplex waveform and as such, modeling using a single sinusoidal wavewill not result in an effective reduction of the waveform, as it mighthave for the LPES waveform shown. It is in such situations where thereduction processes described herein may be most beneficial.

The graph in FIG. 6L illustrates the relative size of the frequencycomponents. This demonstrates that accounting for an AS, through use ofmultiple harmonic sinusoids as is done in the embodiments of the presentdisclosure, will increase the accuracy in cancelling the torquedisruptions of AS spring related disruptions as shown in FIG. 6K.

FIGS. 7A-7K illustrate an example of an approximation technique formotor torque smoothing by building a periodic waveform using sinusoidsthat may be used with embodiments of the present disclosure. Asillustrated, multiple harmonic sinusoids based on harmonics of thesupplemental power source can be combined to form a waveform to reduceor remove the disruptive waveform. As the number of harmonics includedin the approximation of the disruptive waveform increases, the errorbetween the disruptive waveform and the approximated waveform goes tozero.

FIG. 7A illustrates the disruptive waveform to be approximated. It wascreated as a torque waveform generated using a fire-skip-skip pattern.This example waveform has a fundamental period of 270 crank angledegrees.

In some implementations, this engine torque is understood to include afixed component (i.e., a DC term) and a variable component that can berepresented by multiple harmonic sinusoids, including a first harmonic(i.e., fundamental frequency) and other harmonics. The fixed DC termtypically represents the force that propels the vehicle and theharmonics are the unavoidable result of the variation in torquegenerated by an internal combustion engine as its cylinders move throughthe various strokes of a combustion cycle.

In this example, the DC term is the average harmonic contributing torque(about 87 Nm) and the first harmonic, illustrated in FIG. 7C, has thesame fundamental period as the pattern of the disruptive waveform. TheDC term (e.g., 87 Nm) can be added to the first harmonic to create theapproximation shown in FIG. 7B.

The second harmonic, shown in FIG. 7E, oscillates twice in thefundamental period. The second harmonic can be added to the DC term andthe first harmonic to create the approximation shown in FIG. 7D. In thismanner, the approximated waveform can become more similar to thedisruptive waveform as the smaller sinusoids define some of the finerdetails of the disruptive waveform.

As can be seen from these illustrations, the phase or timing of the useof these harmonics is important in building the waveform to reduce oreliminate the disruptive waveform. Accordingly, the phase or timing canbe determined through engine testing and/or sensor data taken fromengine sensors during engine operation.

The third harmonic, shown in FIG. 7G, oscillates three times in thefundamental period. The third harmonic can be added to the DC term andthe first and second harmonics to create the approximation shown in FIG.7F. As can be seen with this and the following smaller waveforms, theuse of these smaller sinusoids moves the error between the approximatedwaveform and the disruptive waveform closer to zero each time a harmonicsinusoid is added to the approximation.

The fifth harmonic, shown in FIG. 7I, oscillates five times in thefundamental period. The fifth harmonic can be added to the DC term andthe first, second, and third harmonics to create the approximation shownin FIG. 7H. Through this addition, there is very little difference intorque between the approximated and disruptive waveforms.

The tenth harmonic, shown in FIG. 7K, oscillates ten times in thefundamental period. The tenth harmonic can be added to the DC term andthe first, second, third, and fifth harmonics to create theapproximation shown in FIG. 7J. Through use of this sinusoid, theapproximation and the disruptive waveforms are very similar and NVHimpact is nearly completely removed and the remaining impact isimperceptible to a vehicle occupant.

Although five harmonics are shown in this example, it may be that lessor more harmonics may be utilized and that different numbers ofharmonics may be used during different engine cycles. Further, theselection of the harmonics used (e.g., 1st, 5th, 10th) is based on abest fit calculation that can be performed by software of the enginecontroller discussed herein, and the best fit calculation can determine,for example, the number of harmonics to be used, the types of harmonicsto be used, and the timing of use of each harmonic.

Such a process can, for example, include selecting a periodic disruptivewaveform to approximate, determine a first harmonic sinusoid from agroup of harmonic sinusoids that reduces the error between anapproximated waveform and the disruptive waveform, and determine atimeframe for utilizing the first harmonic to form a first version of anapproximated waveform. This process can then be repeated to prepare thesubsequent one or more sinusoids to be added to the approximatedwaveform to form subsequent versions of the approximated waveform.

It should be noted that in some embodiments, if the exhaust gasrecirculation (EGR) fraction can be controlled for an individualcylinder, the firing history of that cylinder can be used to set the EGRfraction. For example, if the cylinder was fired the cycle before thecurrent cycle, the EGR fraction can be set to nominal (e.g., apredetermined fraction). If the cylinder was skipped once before thecurrent cycle, the EGR fraction can be set to ½ nominal, and for two ormore skips it can be set to zero. In this manner, the exhaust gas ratherthan air from outside the engine can be provided through the intake.

FIG. 8 is a schematic diagram of an engine controller for an internalcombustion engine for use with embodiments of the present disclosure.FIG. 8 shows a hybrid vehicle control system suitable for controllingthe hybrid vehicle powertrain shown in FIG. 3 according to a particularembodiment. The vehicle control system 850 includes an engine controlunit (ECU) 858, an internal combustion engine 860, a powertrain 859, andan additional power source 857.

The additional power source may include one or more power sources, suchas power electronics, a motor/generator, and/or an energy storagedevice. The ECU 858 can receive input signals 856 representative of thedesired engine output associated with a skipping or recharging event(i.e., during or after the skipping or recharging event as the torquefrom the primary power source recovers).

The input signal 856 may be treated as a request for a desired engineoutput or torque. The signal 856 may be received or derived from anaccelerator pedal position sensor (APP) 861 or other suitable sources,such as a cruise controller, a torque calculator, etc.

An optional preprocessor 854 may modify the accelerator pedal signalprior to delivery to the engine controller 858. However, it should beappreciated that in other implementations, the accelerator pedalposition sensor may communicate directly with the engine controller 858.

The ECU 858 may include a firing sequence generator 862, a torque modelmodule 864, a power train parameter module 866, a firing control unit869, and an NVH reduction module 868. These units and modulescommunicate with each other and work cooperatively to control thevehicle.

The firing sequence generator 862 determines the sequence of skips andfires of the cylinders of engine 860. The firing sequence may begenerated based on a firing fraction and an output of a delta-sigmaconverter or may be generated in any appropriate manner, such as thosedescribed in U.S. Pat. Nos. 8,099,224, 9,086,020, and 9,200,587, whichare incorporated herein by reference in their entirety.

In operation, the firing sequence generator may investigate the fuelefficiency associated with various firing sequences and choose thefiring sequence that offers optimal fuel economy while meeting thetorque request. In some cases, the powertrain torque may be supplementedor reduced by the power source 857.

The output of the firing sequence generator is a drive pulse signal 852that may consist of a bit stream, in which each 0 indicates a skip andeach 1 indicates a fire for an associated cylinder firing opportunitythereby defining a firing sequence. Additionally, if a recharge event isdetermined to be required, a −1 can be transmitted. The firing decisionassociated with any firing opportunity is generated in advance(feedforward) of the firing opportunity to provide adequate time for thefiring control unit 869 to correctly configure the engine 860. Forexample, a firing decision may be to deactivate a cylinder intake valveon a skipped firing opportunity.

The torque model module 864 determines an estimated torque based on thefiring sequence and power train parameters determined by the powertrainparameter module 866. These power train parameters may include, but arenot limited to, intake manifold absolute pressure (MAP), cam phaseangle, spark timing, exhaust gas recirculation level, and engine speed.

The power train parameter module 866 may direct the firing control unit869 to set selected power train parameters appropriately to ensure thatthe actual powertrain output substantially equals the requested output.The firing control unit 869 may also actuate the cylinder firings.

The NVH reduction module 868 may use the output of the torque modelmodule 864 to determine an NVH associated with any particular firingsequence and set of power train parameters. In certain cases, the NVHreduction module 868 may (e.g., based on information about the type ofspring being utilized, the length of time since the last recharge)direct additional power source 857 to add or subtract torque from thepowertrain 859. It should be appreciated that the various modulesdepicted in FIG. 8 may be combined or configured in a different mannerwithout impacting the overall functionality of the vehicle controlsystem 850.

Torque Profile

In order to determine whether it is necessary to supply a smoothingtorque and what that smoothing torque should be, it is advantageous toestimate the overall torque profile of the internal combustion engine.This estimate must be done in an accurate, computationally efficientmanner so that the engine torque profile can be predicted in real time.The predicted torque profile may then be used to determine what, if any,smoothing torque is required.

A single cylinder, normalized torque profile can be used to model theoverall torque profile of a skip-fire controlled internal combustionengine. Normalized profiles for fired, recharging, and skipped cylindersmay be recorded in a look up table. An estimated torque profile for eachcylinder can then be determined based on scaling and shifting thenormalized torque by factors, such as spark cam phase angle, fueling,and number of times the cylinder has been skipped since the last fire orrecharge event. The torque profile can be used, in part, to determinethe additional source/sink torque from 857.

The estimated torque profile for all engine cylinders can be summed withthe appropriate phasing to obtain the overall engine torque profile. Themethod described herein can be used to determine the engine torque witha resolution of 0.5° of crank angle, although as described below,courser resolution can often be used to reduce computational timewithout significantly impacting model accuracy.

FIG. 9 is a logic diagram of a controller arranged to operate aninternal combustion engine that can be used with embodiments of thepresent disclosure. FIG. 9 schematically illustrates a method 990 ofdetermining the most fuel efficient firing sequence according to anembodiment of the present disclosure.

In this method, one or more candidate firing sequences may be generatedby the firing sequence generator (e.g., 862 of FIG. 8). The candidatefiring sequences may be generated by any known method, such as thosedescribed in U.S. Pat. Nos. 8,099,224, 9,086,020, 9,200,587 and9,200,575 and U.S. patent application Ser. Nos. 14/638,908 and14/704,630, which are incorporated herein by reference in theirentirety.

Based on the candidate firing sequences and the determination ofnon-fired (skipped) cylinders, a determination of the timing of rechargeevents can be made at step 991.

The candidate firing sequences and recharge event timing are input intoa torque model 992. Also input into the torque model are various engineparameters, such as spark timing, cam phase angle, engine speed, MAP,fuel, etc.

The torque model 992 determines the torque profile for these rechargeevents at step 993. An assessment may then be made at step 994 whether asmoothing torque is necessary for a skipping event or a recharge eventto provide an acceptable NVH level. The vehicle transmission gearsetting may be used in making this assessment.

If a smoothing torque is not required, the flow diagram can proceed tostep 996. If a smoothing torque is required, an assessment is made atstep 995 whether there is adequate stored or available supplementalenergy from additional sources to supply the smoothing torque.

If insufficient supplemental energy is available, that candidate firingsequence cannot be used and another is analyzed to see if it hassufficient energy. If sufficient supplemental energy is available, thenthe method proceeds to step 996, where the fuel efficiency of theevaluated firing sequences are compared and the firing sequenceproviding optimum fuel efficiency is selected as the operational firingsequence.

The method then proceeds to step 997, where the engine is operating onthe selected operational firing sequence. The method 990 may be repeatedfor each firing opportunity to determine an optimal firing sequence.

Generating a smoothing torque to compensate for internal combustionengine torque variations can be an application of the previouslydescribed torque model. Engine operation variables input to the modelmay include, for example, cam angle (controlling valve timing), MAP,fuel, engine speed, spark timing, crank angle, firing sequence, andfiring fraction. In some implementations, the torque model can generatethe instantaneous engine torque profile.

Knowing the torque profile at a particular crank angle, an enginecontroller may control the smoothing torque needed to be removed fromthe powertrain, for example, by a generator, or added into thepowertrain, for example, by an electric motor. The electricmotor/generator may be integrated into a single unit in communicationwith an electrical energy storage device, such as a battery orcapacitor.

The smoothing torque may, for example, be a band pass filtered versionof the torque profile generated by 992. Using a band pass filter, themostly constant frequencies are ignored, as are the higher frequencies.The resultant filtered waveform can then be appropriately delayed toline up with the motor torque, and then subtracted using, for example,an electric motor. Such usage should remove or reduce the low frequencytorque disturbances associated with skipping or recharging. Rechargingrelated frequencies are typically lower than the frequency componentsthat arise from the DSF firing pattern and, therefore, it can beimportant, from an NVH perspective, to reduce or remove them.

FIG. 10 is a schematic block diagram for a smoothing controller that maybe used with embodiments of the present disclosure. FIG. 10 shows anembodiment of a cancellation method which may be utilized to reduce oreliminate skip and/or recharge related distortions.

Inputs to the method include various engine parameters, such as MAP, camphase angle, engine speed, and spark timing. Another input to the modelis the firing fraction or firing sequence, which defines the pattern ofupcoming skips and fires. These values are input into an engine torquemodel as previously described.

The engine speed and firing information may, for example, be input intoa filter coefficient determination module. The module determines thefilter coefficients for the various DSF orders of interest (for example,the first and second order) to generate the smoothing torque from thetorque profile. In some embodiments, the module may also be used toreduce the NVH of the pattern not including the effect of the recharge.

In some cases, previously used filter coefficients may be used in anupcoming calculation. In such implementations, the future torque profileand filter coefficients can, for example, be input into a filter bank.The filter bank is configured to calculate an appropriate smoothingtorque to cancel, for example, low order torque oscillations in thecrank angle domain that are related to recharge events. The filtercoefficients used in the calculation may be sent to the filtercoefficient determination module for use in a subsequent calculation.

The output of the filter bank may be directed to a crank angle to timedomain conversion module. This module may use the engine speed andcalculated future torque profile to transform the input crank domainsignal to an output time domain signal. The conversion may be simplybased on average engine speed or may optionally include calculated speedvariations based on the calculated torque profile.

Output of the time domain conversion module may be directed to the powerelectronics unit 344 (see FIG. 3) of the motor/generator. The powerelectronics unit 344 controls the motor/generator, which adds orsubtracts torque from the powertrain as specified by the time domainconversion module signal. The resultant powertrain torque has beensmoothed to reduce or remove torque fluctuations from the skipping orrecharge event that would cause undesirable NVH.

Although specific embodiments have been illustrated and describedherein, those of ordinary skill in the art will appreciate that anyarrangement calculated to achieve the same techniques can be substitutedfor the specific embodiments shown. This disclosure is intended to coverany and all adaptations or variations of various embodiments of thedisclosure.

It is to be understood that the above description has been made in anillustrative fashion and not a restrictive one. Combination of the aboveembodiments, and other embodiments not specifically described herein,will be apparent to those of skill in the art upon reviewing the abovedescription.

The scope of the various embodiments of the disclosure includes anyother applications in which the above structures and methods are used.Therefore, the scope of various embodiments of the disclosure should bedetermined with reference to the appended claims, along with the fullrange of equivalents to which such claims are entitled.

In the foregoing Detailed Description, various features are groupedtogether in example embodiments illustrated in the figures for thepurpose of streamlining the disclosure. This method of disclosure is notto be interpreted as reflecting an intention that the embodiments of thedisclosure require more features than are expressly recited in eachclaim.

Rather, as the following claims reflect, inventive subject matter liesin less than all features of a single disclosed embodiment. Thus, thefollowing claims are hereby incorporated into the Detailed Description,with each claim standing on its own as a separate embodiment.

What is claimed:
 1. An engine controller in a vehicle for managing motortorque smoothing, the controller configured to: determine a smoothingevent time period where a particular one of a number of cylinders thathave not been designated to be fired is either skipped or recharged;select a periodic disruptive waveform to approximate that is related toa skip or recharge event that is part of the smoothing event timeperiod; and determine a first harmonic sinusoid from a group of harmonicsinusoids that reduces the error between an approximated waveform andthe disruptive waveform; and initiate a supplemental quantity of torqueduring the smoothing event time period based on the disruption quantityof torque.
 2. The engine controller as recited in claim 1, wherein thecontroller is configured to operate the internal combustion engine at afiring fraction that is less than a value of 1.0, wherein one or morecylinders of the internal combustion engine are not designated to befired.
 3. The engine controller as recited in claim 1, wherein thecontroller is configured to operate when one or more cylinders of theinternal combustion engine are not designated to be fired.
 4. The enginecontroller as recited in claim 1, wherein the controller is configuredto determine a phase or a timeframe for utilizing the first harmonic. 5.The engine controller as recited in claim 1, wherein the controller isconfigured to actuate an additional motor to initiate a supplementalquantity of torque during the smoothing event time period.
 6. The enginecontroller as recited in claim 4, wherein the supplemental quantity oftorque changes over time.
 7. The engine controller as recited in claim4, wherein the engine controller is configured to: determine a secondharmonic sinusoid from a group of harmonic sinusoids that reduces theerror between an approximated waveform and the disruptive waveform; anddetermine a timeframe for utilizing the second harmonic.
 8. A method formanaging motor torque smoothing, the method comprising: determining asmoothing event time period where each of a number of cylinders thathave not been designated to be fired are either skipped or rechargedduring operation of the engine, including firing of the cylindersdesignated for firing; selecting a periodic disruptive waveform toapproximate that is related to a skip or recharge event that is part ofthe smoothing event time period; and providing a supplemental quantityof torque during the smoothing event time period based on theapproximated waveform.
 9. The method as recited in claim 8, wherein themethod includes determining a second harmonic sinusoid from a group ofharmonic sinusoids that reduces the error between an approximatedwaveform and the disruptive waveform.
 10. The method as recited in claim8, wherein the method includes determining a timeframe for utilizing thesecond harmonic.
 11. The method as recited in claim 10, wherein themethod includes determining a number of skip or recharge events for eachcylinder within the smoothing event time period.
 12. The method asrecited in claim 8, wherein the method includes forming an approximatedwaveform that includes a DC term.
 13. The method as recited in claim 12,wherein the method includes forming an approximated waveform thatcombines the DC term and at least one of the first harmonic sinusoid andsecond harmonic sinusoid.
 14. The method as recited in claim 12, whereinthe method includes forming an approximated waveform that includes atleast one of the first harmonic sinusoid and second harmonic sinusoid.15. An engine control system in a vehicle for managing motor torquesmoothing, the system comprising: an internal combustion engine thatprovides power to a drivetrain of a vehicle; an additional power sourcethat provides supplemental power to the drivetrain; and an enginecontroller configured to: determine a smoothing event time period whereeach of a number of cylinders that have not been designated to be firedare either skipped or recharged during operation of the engine, whereinoperation of the engine includes firing of the cylinders designated forfiring; select a periodic disruptive waveform to approximate that isrelated to a skip or recharge event that is part of the smoothing eventtime period; determine a first harmonic sinusoid from a group ofharmonic sinusoids that reduces the error between an approximatedwaveform and the disruptive waveform; and initiate actuation of theadditional power source to supply a supplemental quantity of torquebased on the approximated waveform.
 16. The system as recited in claim15, wherein the supplemental quantity of torque includes at least one ofpositive and negative torque values
 17. The system as recited in claim16, wherein the supplemental quantity of torque is supplied during aperiod of the periodic disruptive waveform.
 18. The system as recited inclaim 16, wherein the supplemental quantity of torque is supplied aftera period of the periodic disruptive waveform.
 19. The system as recitedin claim 15, wherein for each of the cylinders that have not beendesignated to be fired, the engine controller selects a spring mode fromthe group including: low pressure exhaust spring mode, air spring mode,and high pressure exhaust spring mode.
 20. The system as recited inclaim 19, wherein if air spring mode or high pressure exhaust springmode is selected, then one or more smoothing event time periods aredetermined.